Micromixers based on chaotic advection - Micromixers Fundamentals Design and Fabrication - page 202

FIGURE 6.8

Planar micromixers based on Dean flow: (a) curved channels (after [9] ) and (b) 90-degree turns.

a depth of 48 m, and a length of 2 mm were fabricated using excimer laser. Because of the extremely

high pressure, only Reynolds numbers up to 10 can be achieved with this mixer. High pressure above
this Reynolds number will cause leaking. This example shows that mixing at high Reynolds number is
only suitable for processes with available facilities and technology that can handle high pressure.

m

6.2 CHAOTIC ADVECTION AT INTERMEDIATE REYNOLDS NUMBERS
6.2.1 Chaotic advection with 90 turns
Because a 90 turn is the key factor for mixing in a T-mixer at high Reynolds numbers, mixing can be
improved if this 90 turn is repeated in the mixing channel. The two vortices at Dean numbers below
the critical value are still sufficient for improving mixing. Micromixers working in Reynolds number
range 10

100 can well utilize Dean vortices to improve transversal transport.
Yi and Bau investigated Dean flow at a 90 turn in microchannels [11] . The strength of Dean
vortices at an axial position x was defined as

< Re <

ZZ v u 2

vy vy

z Þ¼ d x d y : Uð Re ; (6.2)

vx

The star indicates that the variables are dimensionless. The spatial variables are normalized by the
hydraulic diameter of the channel. Fitting the numerical data results in the following function of vortex
strength after a 90 turn [11] :
Uð Re z Þ¼Uð Re 5 Þ exp ½f ð Re Þðz 0 ; ; 0 : : 5 Þ (6.3)

with

5Re 0 : 27 f ð Re Þw 7 : (6.4)